Optimal Multistage Algorithm for Adjoint Computation

Guillaume Aupy (1, 2, 3) , Julien Herrmann (2, 3) , Paul Hovland (4) , Yves Robert (5, 2, 3)

1 Vanderbilt University [Nashville]
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 ROMA - Optimisation des ressources : modèles, algorithmes et ordonnancement
4 MCS - Mathematics and Computer Science Division [ANL]
5 Department of Computer Science. University of Tennessee

We reexamine the work of Stumm and Walther on multistage algorithms for adjoint computation. We provide an optimal algorithm for this problem when there are two levels of checkpoints, in memory and on disk. Previously, optimal algorithms for adjoint computations were known only for a single level of checkpoints with no writing and reading costs; a well-known example is the binomial checkpointing algorithm of Griewank and Walther. Stumm and Walther extended that binomial checkpointing algorithm to the case of two levels of checkpoints, but they did not provide any optimality results. We bridge the gap by designing the first optimal algorithm in this context. We experimentally compare our optimal algorithm with that of Stumm and Walther to assess the difference in performance.

Domaines: Algorithme et structure de données [cs.DS]; Logiciel mathématique [cs.MS]

Guillaume Aupy, Julien Herrmann, Paul Hovland, Yves Robert. Optimal Multistage Algorithm for Adjoint Computation. [Research Report] RR-8721, LIP - ENS Lyon; Argonne National Laboratory; INRIA; Vanderbilt University. 2014. ⟨hal-01147155v2⟩